Table 3 Estimation results of GARCH and APARCH models with Student’s t-distribution

μ

1.79E-07

6.72E-08

−4.08E-08

7.92E-10

4.36E-09

2.25E-09

(1.37E-07)

(1.42E-07)

(1.56E-07)

(1.84E-07)

(1.03E-07)

(6.09E-08)

ρ ₁

0.227924*

0.246680*

0.149727*

0.095646*

(0.022967)

(0.018652)

(0.016292)

(0.011675)

ρ ₂

0.166564*

0.073848*

(0.016849)

(0.009821)

η

2.76E-13

2.01E-13

1.78E-13

0.000808

2.70E-05

0.000190

(2.08E-13)

(1.50E-13)

(1.12E-13)

(0.000809)

(6.55E-05)

(0.000549)

α

0.926099*

1.889860*

1.633760*

1.421359**

1.707541*

1.445461*

(0.073253)

(0.426702)

(0.452555)

(0.669212)

(0.501460)

(0.506596)

γ

−0.068862**

−0.078959***

−0.106666**

(0.032925)

(0.041074)

(0.044544)

δ

0.611742*

0.671478*

0.530577*

(0.021520)

(0.028684)

(0.019776)

β

0.464984*

0.514459*

0.503470*

0.653877*

0.574994*

0.593071*

(0.004546)

(0.004297)

(0.004305)

(0.008688)

(0.012415)

(0.009463)

Q1(4)

0.0032

0.0015

0.0015

0.0002

0.00002

0.000004

Q1(8)

0.0064

0.0029

0.0030

0.0231

0.00003

0.00001

Q2(4)

0.0321

0.0268

0.0270

0.0802

0.0569

0.0551

Q2(8)

0.0644

0.0538

0.0542

0.1603

0.1142

0.1105

Log Likelihood

6606.627

6622.211

6690.907

6717.160

7694.906

7809.244

F Statistic

0.007976

0.00666

0.006713

0.01994

0.01414

0.013687

Probability

0.9288

0.9349

0.9347

0.8877

0.9053

0.9069